1,471 research outputs found
Predictability: a way to characterize Complexity
Different aspects of the predictability problem in dynamical systems are
reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy,
Shannon entropy and algorithmic complexity is discussed. In particular, we
emphasize how a characterization of the unpredictability of a system gives a
measure of its complexity. Adopting this point of view, we review some
developments in the characterization of the predictability of systems showing
different kind of complexity: from low-dimensional systems to high-dimensional
ones with spatio-temporal chaos and to fully developed turbulence. A special
attention is devoted to finite-time and finite-resolution effects on
predictability, which can be accounted with suitable generalization of the
standard indicators. The problems involved in systems with intrinsic randomness
is discussed, with emphasis on the important problems of distinguishing chaos
from noise and of modeling the system. The characterization of irregular
behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports.
Related information at this http://axtnt2.phys.uniroma1.i
Quantum fluctuations and life
There have been many claims that quantum mechanics plays a key role in the
origin and/or operation of biological organisms, beyond merely providing the
basis for the shapes and sizes of biological molecules and their chemical
affinities. These range from the suggestion by Schrodinger that quantum
fluctuations produce mutations, to the conjecture by Hameroff and Penrose that
quantum coherence in microtubules is linked to consciousness. I review some of
these claims in this paper, and discuss the serious problem of decoherence. I
advance some further conjectures about quantum information processing in
bio-systems. Some possible experiments are suggested.Comment: 10 pages, no figures, conference pape
Path-sum solution of the Weyl Quantum Walk in 3+1 dimensions
We consider the Weyl quantum walk in 3+1 dimensions, that is a discrete-time
walk describing a particle with two internal degrees of freedom moving on a
Cayley graph of the group , that in an appropriate regime evolves
according to Weyl's equation. The Weyl quantum walk was recently derived as the
unique unitary evolution on a Cayley graph of that is homogeneous
and isotropic. The general solution of the quantum walk evolution is provided
here in the position representation, by the analytical expression of the
propagator, i.e. transition amplitude from a node of the graph to another node
in a finite number of steps. The quantum nature of the walk manifests itself in
the interference of the paths on the graph joining the given nodes. The
solution is based on the binary encoding of the admissible paths on the graph
and on the semigroup structure of the walk transition matrices.Comment: 13 page
Fashion, Cooperation, and Social Interactions
Fashion plays such a crucial rule in the evolution of culture and society
that it is regarded as a second nature to the human being. Also, its impact on
economy is quite nontrivial. On what is fashionable, interestingly, there are
two viewpoints that are both extremely widespread but almost opposite:
conformists think that what is popular is fashionable, while rebels believe
that being different is the essence. Fashion color is fashionable in the first
sense, and Lady Gaga in the second. We investigate a model where the population
consists of the afore-mentioned two groups of people that are located on social
networks (a spatial cellular automata network and small-world networks). This
model captures two fundamental kinds of social interactions (coordination and
anti-coordination) simultaneously, and also has its own interest to game
theory: it is a hybrid model of pure competition and pure cooperation. This is
true because when a conformist meets a rebel, they play the zero sum matching
pennies game, which is pure competition. When two conformists (rebels) meet,
they play the (anti-) coordination game, which is pure cooperation. Simulation
shows that simple social interactions greatly promote cooperation: in most
cases people can reach an extraordinarily high level of cooperation, through a
selfish, myopic, naive, and local interacting dynamic (the best response
dynamic). We find that degree of synchronization also plays a critical role,
but mostly on the negative side. Four indices, namely cooperation degree,
average satisfaction degree, equilibrium ratio and complete ratio, are defined
and applied to measure people's cooperation levels from various angles. Phase
transition, as well as emergence of many interesting geographic patterns in the
cellular automata network, is also observed.Comment: 21 pages, 12 figure
Metric characterization of cluster dynamics on the Sierpinski gasket
We develop and implement an algorithm for the quantitative characterization
of cluster dynamics occurring on cellular automata defined on an arbitrary
structure. As a prototype for such systems we focus on the Ising model on a
finite Sierpsinski Gasket, which is known to possess a complex thermodynamic
behavior. Our algorithm requires the projection of evolving configurations into
an appropriate partition space, where an information-based metrics (Rohlin
distance) can be naturally defined and worked out in order to detect the
changing and the stable components of clusters. The analysis highlights the
existence of different temperature regimes according to the size and the rate
of change of clusters. Such regimes are, in turn, related to the correlation
length and the emerging "critical" fluctuations, in agreement with previous
thermodynamic analysis, hence providing a non-trivial geometric description of
the peculiar critical-like behavior exhibited by the system. Moreover, at high
temperatures, we highlight the existence of different time scales controlling
the evolution towards chaos.Comment: 20 pages, 8 figure
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